`quat` Class Template

Quaternion with scalar part w and vector part v. More...

Declaration

template <typename T> class helios::math::quat<T> { ... }

Public Constructors Index

template <typename T>
constexpr	quat (const vec3< T > v, const T w) noexcept
	Constructs a quaternion from vector and scalar parts. More...

Public Operators Index

template <typename T>
auto	operator* (const quat< T > &other) const noexcept -> constexpr quat< T >
	Multiplies this quaternion by another quaternion. More...

Public Member Functions Index

template <typename T>
auto	conjugate () const noexcept -> constexpr quat< T >
	Returns the quaternion conjugate. More...

template <typename T>
constexpr T	w () const noexcept
	Returns the scalar part. More...

template <typename T>
auto	v () const noexcept -> constexpr vec3< T >
	Returns the vector part. More...

template <typename T>
constexpr T	length () const noexcept
	Returns the Euclidean norm of the quaternion. More...

template <typename T>
auto	normalized () const noexcept -> constexpr quat< T >
	Returns a normalized copy of the quaternion. More...

template <typename T>
auto	rotationMatrix () const noexcept -> constexpr mat4< T >
	Converts the (normalized) quaternion to a 4x4 rotation matrix. More...

template <typename T>
auto	rotate (const vec3< T > v) const noexcept -> constexpr vec3< T >
	Rotates a vector by this (normalized) quaternion. More...

Private Member Attributes Index

template <typename T>
T	w_


template <typename T>
vec3< T >	v_

Public Static Functions Index

template <typename TFrameRelation>
static auto	fromEulerAngles (const T xAngle, const T yAngle, const T zAngle) noexcept -> constexpr quat< T >
	Creates a quaternion from Euler angles. More...

template <typename T>
static auto	identity () noexcept -> constexpr quat< T >
	Returns the identity quaternion. More...

template <typename T>
static auto	fromAxisAngle (const helios::math::vec3< T > v, const T angle) noexcept -> constexpr quat< T >
	Creates a quaternion from axis-angle representation. More...

Description

Quaternion with scalar part w and vector part v.

Template Parameters

T	Floating-point scalar type.

Definition at line 36 of file quat.ixx.

Public Constructors

quat()

template <typename T>

constexpr helios::math::quat< T >::quat (const vec3< T > v, const T w)

inline explicit constexpr noexcept

Constructs a quaternion from vector and scalar parts.

Parameters

v	Vector (imaginary) part.
w	Scalar (real) part.

Definition at line 103 of file quat.ixx.

103 explicit constexpr quat(const vec3<T> v, const T w) noexcept

104 : w_(w), v_(v) {}

Public Operators

operator*()

template <typename T>

constexpr quat< T > helios::math::quat< T >::operator* (const quat< T > & other)

inline constexpr noexcept

Multiplies this quaternion by another quaternion.

Parameters

other

Right-hand quaternion operand.

Returns: Product quaternion.

Definition at line 113 of file quat.ixx.

113 constexpr quat<T> operator*(const quat<T>& other) const noexcept {

114

115 const auto v = v_.cross(other.v_) + w_ * other.v_ + other.w_ * v_;

116

117 const auto w = w_ * other.w_ - dot(v_, other.v_);

118

119 return quat<T>{v, w};

120 }

References helios::math::vec3< T >::cross, helios::math::dot, helios::math::quat< T >::v and helios::math::quat< T >::w.

Public Member Functions

conjugate()

template <typename T>

constexpr quat< T > helios::math::quat< T >::conjugate ()

inline constexpr noexcept

Returns the quaternion conjugate.

Returns: Conjugated quaternion with negated vector part.

Definition at line 127 of file quat.ixx.

127 [[nodiscard]] constexpr quat<T> conjugate() const noexcept {

128 return quat<T>{v_ * static_cast<T>(-1), w_};

129 }

length()

template <typename T>

constexpr T helios::math::quat< T >::length ()

inline constexpr noexcept

Returns the Euclidean norm of the quaternion.

Returns: Quaternion length.

Definition at line 155 of file quat.ixx.

155 [[nodiscard]] constexpr T length() const noexcept {

156 return static_cast<T>(std::sqrt(

157 v_[0] * v_[0] + v_[1] * v_[1] + v_[2] * v_[2] + w_ * w_

158 ));

159 }

Referenced by helios::math::quat< T >::normalized.

normalized()

template <typename T>

constexpr quat< T > helios::math::quat< T >::normalized ()

inline constexpr noexcept

Returns a normalized copy of the quaternion.

Returns: Unit-length quaternion.

Definition at line 166 of file quat.ixx.

166 [[nodiscard]] constexpr quat<T> normalized() const noexcept {

167 const auto l = length();

168 return quat<T>{v_ * (static_cast<T>(1) / l), w_ / l};

169 }

Reference helios::math::quat< T >::length.

Referenced by helios::math::quat< T >::fromEulerAngles, helios::math::quat< T >::rotate and helios::math::quat< T >::rotationMatrix.

rotate()

template <typename T>

constexpr vec3< T > helios::math::quat< T >::rotate (const vec3< T > v)

inline constexpr noexcept

Rotates a vector by this (normalized) quaternion.

Parameters

v	Vector to rotate.

Returns: Rotated vector.

Definition at line 222 of file quat.ixx.

222 [[nodiscard]] constexpr vec3<T> rotate(const vec3<T> v) const noexcept {

223 const auto q_norm = normalized();

224 const auto other = quat<T>{v, 0};

225

226 return (q_norm * other * q_norm.conjugate()).v() ;

227 }

References helios::math::quat< T >::normalized and helios::math::quat< T >::v.

rotationMatrix()

template <typename T>

constexpr mat4< T > helios::math::quat< T >::rotationMatrix ()

inline constexpr noexcept

Converts the (normalized) quaternion to a 4x4 rotation matrix.

Returns: Rotation matrix derived from the normalized quaternion.

Definition at line 176 of file quat.ixx.

176 [[nodiscard]] constexpr mat4<T> rotationMatrix() const noexcept {

177

178 const auto q_norm = normalized();

179 const auto v = q_norm.v();

180 const auto w = q_norm.w();

181

182 const auto x2 = v[0] * v[0];

183 const auto y2 = v[1] * v[1];

184 const auto z2 = v[2] * v[2];

185 const auto xy = v[0] * v[1];

186 const auto xz = v[0] * v[2];

187 const auto yz = v[1] * v[2];

188 const auto wx = w * v[0];

189 const auto wy = w * v[1];

190 const auto wz = w * v[2];

191

192 return mat4<T>{

193 static_cast<T>(1) - static_cast<T>(2) * (y2 + z2),

194 static_cast<T>(2) * (xy + wz),

195 static_cast<T>(2) * (xz - wy),

196 static_cast<T>(0),

197

198 static_cast<T>(2) * (xy - wz),

199 static_cast<T>(1) - static_cast<T>(2) * (x2 + z2),

200 static_cast<T>(2) * (yz + wx),

201 static_cast<T>(0),

202

203 static_cast<T>(2) * (xz + wy),

204 static_cast<T>(2) * (yz - wx),

205 static_cast<T>(1) - static_cast<T>(2) * (x2 + y2),

206 static_cast<T>(0),

207

208 static_cast<T>(0),

209 static_cast<T>(0),

210 static_cast<T>(0),

211 static_cast<T>(1)

212 };

213

214 }

References helios::math::quat< T >::normalized, helios::math::quat< T >::v and helios::math::quat< T >::w.

v()

template <typename T>

constexpr vec3< T > helios::math::quat< T >::v ()

inline constexpr noexcept

Returns the vector part.

Returns: Vector component v.

Definition at line 146 of file quat.ixx.

146 [[nodiscard]] constexpr vec3<T> v() const noexcept {

147 return v_;

148 }

Referenced by helios::math::quat< T >::fromAxisAngle, helios::math::quat< T >::operator*, helios::math::quat< T >::rotate and helios::math::quat< T >::rotationMatrix.

w()

template <typename T>

constexpr T helios::math::quat< T >::w ()

inline constexpr noexcept

Returns the scalar part.

Returns: Scalar component w.

Definition at line 137 of file quat.ixx.

137 [[nodiscard]] constexpr T w() const noexcept {

138 return w_;

139 }

Referenced by helios::math::quat< T >::operator* and helios::math::quat< T >::rotationMatrix.

Private Member Attributes

v_

template <typename T>

vec3<T> helios::math::quat< T >::v_

Definition at line 40 of file quat.ixx.

40 vec3<T> v_;

w_

template <typename T>

T helios::math::quat< T >::w_

Definition at line 38 of file quat.ixx.

38 T w_;

Public Static Functions

fromAxisAngle()

template <typename T>

constexpr quat< T > helios::math::quat< T >::fromAxisAngle (const helios::math::vec3< T > v, const T angle)

inline constexpr noexcept static

Creates a quaternion from axis-angle representation.

Parameters

v	Rotation axis (normalized internally).
angle	Rotation angle in radians.

Returns: Quaternion representing the axis-angle rotation.

Definition at line 86 of file quat.ixx.

86 static constexpr quat<T> fromAxisAngle(const helios::math::vec3<T> v, const T angle) noexcept {

88 const auto rad = angle * static_cast<T>(0.5);

90 return quat<T>{

91 std::sin(rad) * v.normalize(),

92 std::cos(rad)

93 };

95 }

Reference helios::math::quat< T >::v.

Referenced by helios::math::quat< T >::fromEulerAngles.

fromEulerAngles()

template <typename TFrameRelation>

constexpr quat< T > helios::math::quat< T >::fromEulerAngles (const T xAngle, const T yAngle, const T zAngle)

inline constexpr noexcept static

Creates a quaternion from Euler angles.

Template Parameters

TFrameRelation

Rotation composition mode (Intrinsic or Extrinsic).

Parameters

xAngle	Rotation angle around the x-axis in radians.
yAngle	Rotation angle around the y-axis in radians.
zAngle	Rotation angle around the z-axis in radians.

Returns: Quaternion representing the composed rotation.

Definition at line 56 of file quat.ixx.

56 static constexpr quat<T> fromEulerAngles(const T xAngle, const T yAngle, const T zAngle) noexcept {

58 const auto x = vec3<T>{static_cast<T>(1), static_cast<T>(0), static_cast<T>(0)};

59 const auto y = vec3<T>{static_cast<T>(0), static_cast<T>(1), static_cast<T>(0)};

60 const auto z = vec3<T>{static_cast<T>(0), static_cast<T>(0), static_cast<T>(1)};

62 if constexpr (std::same_as<TFrameRelation, Intrinsic>) {

63 return (fromAxisAngle(x, xAngle) * fromAxisAngle(y, yAngle) * fromAxisAngle(z, zAngle)).normalized();

64 } else {

65 return (fromAxisAngle(z, zAngle) * fromAxisAngle(y, yAngle) * fromAxisAngle(x, xAngle)).normalized();

66 }

68 }

References helios::math::quat< T >::fromAxisAngle and helios::math::quat< T >::normalized.

identity()

template <typename T>

constexpr quat< T > helios::math::quat< T >::identity ()

inline constexpr noexcept static

Returns the identity quaternion.

Returns: Quaternion representing no rotation.

Definition at line 75 of file quat.ixx.

75 static constexpr quat<T> identity() noexcept {

76 return quat<T>{vec3<T>{static_cast<T>(0), static_cast<T>(0), static_cast<T>(0)}, static_cast<T>(1)};

77 }

The documentation for this class was generated from the following file:

quat.ixx

Generated via doxygen2docusaurus 2.0.0 by Doxygen 1.9.8.

Declaration​

Public Constructors Index​

Public Operators Index​

Public Member Functions Index​

Private Member Attributes Index​

Public Static Functions Index​

Description​

Public Constructors​

quat()​

Public Operators​

operator*()​

Public Member Functions​

conjugate()​

length()​

normalized()​

rotate()​

rotationMatrix()​

v()​

w()​

Private Member Attributes​

v_​

w_​

Public Static Functions​

fromAxisAngle()​

fromEulerAngles()​

identity()​

Declaration

Public Constructors Index

Public Operators Index

Public Member Functions Index

Private Member Attributes Index

Public Static Functions Index

Description

Public Constructors

quat()

Public Operators

operator*()

Public Member Functions

conjugate()

length()

normalized()

rotate()

rotationMatrix()

v()

w()

Private Member Attributes

v_

w_

Public Static Functions

fromAxisAngle()

fromEulerAngles()

identity()